Gravity, stability and cosmological models

Stability analysis plays a major rule in our understanding of nature. For example it was shown that among empty flat spacetimes only those with a Lorentzian metric are stable [A. Yahalom, Found Phys. 38 (2008) 489-497; Int. J. Mod. Phys. D 18(4) (2009) 2155-2158]. However, the universe is not empty and the energy momentum tensor is metric dependent an thus effects stability. In this essay we concentrate on simple perturbations of the standard cosmological model with and without cosmological constant which is based on a uniform mass distribution. The results suggest that while Euclidean, open or closed section models are valid solutions, the choice of stable solutions is limited. In particular, the popular Lambda-CDM model is unstable.